Remember (from the prologue): the hotter the water, the more compounds will be dissolved, and at a faster rate. Increasing the water temperature increases the temperature of the compounds themselves, which in turn increases their solubility.
In this video, Matt talks temperatures and the Arrhenius Equation
Temperature Equilibrium Calculator
This average brew water temperature calculator will help you consider the implications of changing your brew method and the change to brew water temperature that follows from that change. This will help you predict the difference in starting temperature needed to hit the same average brew water temperature.